Question4. Graph the function $y=2^{x}$ on the domain $0 \leq x \leq 3$. a) Explain why a person who sees only the graph you created (not the equation) might think that the graph represents a polynomial function. b) Explain why this function is not a polynomial function.

Studdy Solution
Explain why the function is not a polynomial function.
- A polynomial function is defined as a sum of terms of the form $ax^n$ where $n$ is a non-negative integer. - The function $y = 2^x$ is an exponential function, where the variable $x$ is in the exponent, not the base. - Exponential functions grow at a rate proportional to their current value, unlike polynomial functions which grow at a rate determined by the highest power of $x$.
The graph might be mistaken for a polynomial due to its smooth, continuous nature over a limited domain, but it is not a polynomial because it is defined by an exponential expression, not a sum of powers of $x$.